Question

comparing relative frequency tables
using the data below, eve created a conditional relative frequency table by column and bob created a conditional relative frequency table by row.

	enjoys dancing	does not enjoy dancing	total
girls	40	10	50
total	60	40	100

which statements are true? check all that apply.

• ☐ based on both tables, there is no association between gender and enjoying dancing.
• ☐ eves table shows that those who enjoy dancing are likely girls.
• ☐ bobs table shows that boys are likely to not enjoy dancing.
• ☐ the two tables will be identical since boys and girls have the same total number.
• ☐ the percentage of someone being a girl, given that the person enjoys dancing is lower than the percentage that someone enjoys dancing, given that the person is a girl.

Explanation:

Step1: Analyze each statement

• Statement 1: Check association. For boys, enjoy dancing: \( \frac{20}{50} = 0.4 \), not enjoy: \( \frac{30}{50} = 0.6 \). For girls, enjoy: \( \frac{40}{50} = 0.8 \), not enjoy: \( \frac{10}{50} = 0.2 \). There is an association (different proportions), so this is false.
• Statement 2: Eve's table (by column). For "Enjoys Dancing" column: girls are \( \frac{40}{60} \approx 0.67 \), boys \( \frac{20}{60} \approx 0.33 \). So those who enjoy dancing are likely girls. True.
• Statement 3: Bob's table (by row). For boys' row: not enjoy is \( \frac{30}{50} = 0.6 \), enjoy is \( 0.4 \). So boys likely not enjoy. True.
• Statement 4: Conditional tables by row vs column differ. Even with same total, row and column percentages differ. False.
• Statement 5: \( P(\text{girl}|\text{enjoy}) = \frac{40}{60} \approx 0.67 \), \( P(\text{enjoy}|\text{girl}) = \frac{40}{50} = 0.8 \). \( 0.67 < 0.8 \), so this is true.

Step2: Identify true statements

True statements: Eve's table shows...; Bob's table shows...; The percentage of...

Answer:

• Eve's table shows that those who enjoy dancing are likely girls.
• Bob's table shows that boys are likely to not enjoy dancing.
• The percentage of someone being a girl, given that the person enjoys dancing is lower than the percentage that someone enjoys dancing, given that the person is a girl.